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A193741 Mirror of the triangle A193740.

%I A193741 #5 Mar 30 2012 18:57:38
%S A193741 1,1,1,3,3,1,9,9,4,1,19,19,10,4,1,34,34,20,10,4,1,55,55,35,20,10,4,1,
%T A193741 83,83,56,35,20,10,4,1,119,119,84,56,35,20,10,4,1,164,164,120,84,56,
%U A193741 35,20,10,4,1,219,219,165,120,84,56,35,20,10,4,1,285,285,220,165
%N A193741 Mirror of the triangle A193740.
%C A193741 A193741 is obtained by reversing the rows of the triangle A193740.
%F A193741 Write w(n,k) for the triangle at A193740.  The triangle at A193741 is then given by w(n,n-k).
%e A193741 First six rows:
%e A193741 1
%e A193741 1....1
%e A193741 3....3....1
%e A193741 9....9....4....1
%e A193741 19...19...10...4...1
%e A193741 34...34...20...10..4..1
%t A193741 z = 12;
%t A193741 p[0, x_] := 1
%t A193741 p[n_, x_] := n + Sum[(k + 1) x^(n - k), {k, 0, n - 1}]
%t A193741 q[n_, x_] := p[n, x]
%t A193741 t[n_, k_] := Coefficient[p[n, x], x^(n - k)];
%t A193741 t[n_, n_] := p[n, x] /. x -> 0;
%t A193741 w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
%t A193741 g[n_] := CoefficientList[w[n, x], {x}]
%t A193741 TableForm[Table[Reverse[g[n]], {n, -1, z}]]
%t A193741 Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193740 *)
%t A193741 TableForm[Table[g[n], {n, -1, z}]]
%t A193741 Flatten[Table[g[n], {n, -1, z}]]   (* A193741 *)
%Y A193741 Cf. A193740.
%K A193741 nonn,tabl
%O A193741 0,4
%A A193741 _Clark Kimberling_, Aug 04 2011